Joan Ostojic's daughters Katherine, 21 and Alice, 19, were on a boat carrying 25 people that went down as it was sailing between Lombok and the Komodo Islands in eastern Indonesia, the Press Association reports.

Mrs Ostojic, of Stevenage, Hertfordshire, said: "It's a relief that they are safe. They are fine, carrying on with their travels and will be home shortly."

She said the girls had emailed her saying that after the boat sank in the middle of the night, they sat on its roof while it was semi-submerged for 10 hours, then swam eight hours to the shore before seeing the lights of some fishermen and being rescued.

The Foreign Office said that student Katherine joined Alice for a month in Indonesia. Alice has been travelling through Australia and south east Asia as part of her gap year.

After being rescued, the girls spent the night on an uninhabited volcanic island where the fishermen gave them food and water, before they were taken to Bima in Sumbawa.

The girls lost everything in the accident apart from their passports, debit cards and cash.

One survivor has said that he had to drink his own urine and eat leaves, but the girls told Mrs Ostojic that they did not have to do that.

Tourists from New Zealand, Spain, France, Switzerland and the Netherlands were also among those rescued after the boat hit a reef in bad weather during the three-day journey.